We have theoretically investigated the crystal orientation effects on the direct band-to-band tunneling probability, and the performance of a 5-nm diameter Ge n-channel nanowire tunnel field-effect transistor (FET). Bulk Ge has indirect band gap, and therefore, its application in tunnel FET is not promising. We study the complex band structures of Ge nanowires in different orientations and showthat the (011) Ge nanowire can be a potential candidate for tunneling FET (TFET). The (001) and (111) nanowires exhibit indirect gaps of 1.07 and 0.966 eV, respectively. In the (001) nanowire, the two X valleys project to the 1-D zone edge and form the conduction band minima. The other X valleys project to the zone center at 0.14 eV above the conduction band minimum. The L[111] and L[ $\overline {{1}}\overline {{1}}\overline {{1}}$ ] valleys project to the zone edge and form conduction band minima in the (111) nanowire. On the other hand, the (011) wire has a direct gap of 0.94 eV due to the projection of L[ $1\overline {{1}}1$ ], L[ $1\overline {{1}}\overline {{1}}$ ], L[ $\overline {{1}} 1\overline {{1}}$ ], and L[ $\overline {{1}}11$ ] valleys to the zone center. Among the three orientations, the (011) wire has the smallest area of the imaginary wave vector that directly connects the band edges at zone center. That is, the (011) wire has the highest direct band-to-band tunneling probability, and therefore, it is a potential candidate for TFETs. We simulate a (011)Ge-(011)Si heterojunction cylindrical nanowire TFET. The staggered band alignment at the heterointerface removes the ambipolar characteristics. The smallest action integral of the (011)Ge wire combined with the shorter tunnel path at the heterointerface results in high drive current for both ${V}_{\text {DD}} = {0.6}$ and 0.4 V. However, the turn-ON behavior with ${V}_{\text {DD}} = {0.4}$ V is superior, which suggests that the proposed nanowire TFET is suitable for low power applications.